A102817 Decimal expansion of Gamma(delta)^2 where delta is the Feigenbaum bifurcation velocity constant (A006890).

2, 1, 7, 9, 9, 9, 9, 7, 6, 4, 4, 9, 9, 9, 8, 8, 1, 4, 6, 8, 6, 2, 8, 8, 1, 3, 9, 5, 7, 7, 9, 3, 6, 0, 9, 8, 9, 0, 7, 2, 6, 7, 9, 7, 8, 9, 0, 9, 7, 3, 0, 0, 5, 6, 5, 4, 8, 3, 2, 8, 8, 5, 2, 1, 2, 2, 4, 0, 4, 2, 3, 7, 7, 2, 0, 9, 6, 4, 2, 6, 1, 4, 9, 8, 3, 9, 2, 3, 1, 1, 2, 6, 8, 1, 5, 0, 7, 1, 6, 5, 3, 3, 0, 8, 6

Offset

3,1

Comments

Let x be this constant, then Integral_{t=1..x} sin(t)/sqrt(t) dt = 0.655555692248871113068...

delta^2 = 21.8014436664499573..., (delta/Gamma(delta))^2 = 0.10000663312663433933000349...

If s is solution of Gamma(s) - sqrt(218) = 0 then 1/((s - delta)*Gamma(delta)^6) = 2.5555951358396... whereas a^(Pi/4) = 2.055596478435... where a is Feigenbaum alpha constant (A006891), the difference = 0.4999986574... ~ 1/(2 + 10^-5.27)

10*cos(Gamma(delta)^2) + Pi = -0.199999019922688714710053...

Links

Table of n, a(n) for n=3..107.

D. Broadhurst, Feigenbaum constants to 1018 decimal places

Example

217.99997644999881468628813957793609890726797890973...

Mathematica

Set delta then RealDigits[Gamma[delta]^2, 10, 110][[1]]

Prog

(PARI) acos(Pi/10+.0199999019922688714710053)+69*Pi \\ Yields ~ 30 digits. Using (2e5-1)/(1e7-1) yields ~ 15 digits. For a better value use, e.g., delta from the Broadhurst link. - M. F. Hasler, Apr 30 2018

Crossrefs

Cf. A006890, A006891.

Sequence in context: A141513 A258058 A238223 * A026252 A032298 A032210

Adjacent sequences: A102814 A102815 A102816 * A102818 A102819 A102820

Keyword

cons,nonn

Author

Gerald McGarvey, Feb 26 2005

Status

approved